Very weak zero-phonon absorption lines were detected and measured in KI crystals containing S2− or Se2− impurities at 2°K, using a newly developed sensitive absorption apparatus. Each impurity caused the same type of absorption spectrum, consisting of two upper-state progressions corresponding to transitions to two sets of vibrationally excited levels in the excited state. Quantum numbers for these levels were determined by isotope shift measurements, and a complete set of spectroscopic constants was calculated. By combining these results with previously reported emission results for the same system a possible energy level scheme was worked out, and the crystal field splittings in both ground and excited states calculated.